Work

On a variant of Hilbert’s 16th problem

Year: 2024

Type: article

Abstract: We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m ⩽ 10 .

Source: Nonlinearity

DOI: 10.1088/1361-6544/ad8c1b

Authors: Armengol Gasull, Paulo Santana

Institutions: Universitat Autònoma de Barcelona, Centre de Recerca Matemàtica, Instituto de Biociências, Letras e Ciências Exatas, câmpus de São José do Rio Preto, Universidade Estadual Paulista (Unesp)

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Agència de Gestió d'Ajuts Universitaris i de Recerca, Agencia Estatal de Investigación

Awards: G1694479832, G5679345223, G6372389125